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An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers

Author

Listed:
  • Idris Ahmed

    (KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematics and Computer Science, Sule Lamido University, P.M.B 048 Kafin-Hausa, Jigawa State, Nigeria)

  • Poom Kumam

    (KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Gafurjan Ibragimov

    (Institute for Mathematical Research and Department of Mathematics, Faculty of Science (FS), Universiti Putra Malaysia, Selangor, Serdang 43400, Malaysia)

  • Jewaidu Rilwan

    (KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, P.M.B 3011 Kano, Nigeria)

  • Wiyada Kumam

    (Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand)

Abstract

The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in l 2 -space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result.

Suggested Citation

  • Idris Ahmed & Poom Kumam & Gafurjan Ibragimov & Jewaidu Rilwan & Wiyada Kumam, 2019. "An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:842-:d:266270
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    References listed on IDEAS

    as
    1. Ibragimov, Gafurjan I. & Salimi, Mehdi & Amini, Massoud, 2012. "Evasion from many pursuers in simple motion differential game with integral constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 505-511.
    2. Gafurjan Ibragimov & Nu'man Satimov, 2012. "A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, November.
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    Cited by:

    1. Jewaidu Rilwan & Pasquale Fotia & Massimiliano Ferrara, 2023. "On game value of a differential game problem with Grönwall-type constraints on players control functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 319-333, June.

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